I had a rear wheel stud snap when backing out a lug nut. This gave me the opportunity to learn how to replace one. I never had before, though I imagined what it could take. Would I have to remove the axle? How about the diff cover to remove a clip or something? How about the rear brakes?
I have a 2001 Jeep Wrangler (TJ) with optional Dana 44 (3.73s).
After doing some research I came up with a few things. Some say the axle needs to go.
I heard with a Dana 44 no clip to remove.
Some say rear brakes need to go. 
Turns out I didn't need to remove the axle, clips or brakes.
This is going to be easy.
I am not an expert. This thread is just documentation of what I did.
1.
Chalked the front wheels. Jacked up rear and put on jack stands. I then removed the wheel and drum.
2.
Sprayed some penetrate on the stud shielding the surrounding areas from over spray.
3.
Hammered it out with a 2 pound hammer. A dead blow hammer may have worked well, but I didn't have one. I placed a piece of 2x4 against the end of the axle to guide the hammer to the stud (not pictured, I only have 2 hands!).
Here's a picture of the old and new stud.
4.
Turned the axle until the hole was lined up with an area where the breaks had enough room to slide the stud in from the back.
5.
Put on several washers and an open end lug nut. I used the flat side against the washers. Tightened to specified torque. As it tightened it drew the stud into the axle flange.
I then removed the nut and washers. Measured the length of the stud against the others. It was the same length.
7.
Put drum and wheel back on. Took vehicle off jack stands. Unchalked front wheels. I used anti-seize on the lug nuts and tightened 20% less than specified torque.
Fin!
I have a 2001 Jeep Wrangler (TJ) with optional Dana 44 (3.73s).
After doing some research I came up with a few things. Some say the axle needs to go.
Turns out I didn't need to remove the axle, clips or brakes.
I am not an expert. This thread is just documentation of what I did.
1.
Chalked the front wheels. Jacked up rear and put on jack stands. I then removed the wheel and drum.
2.
Sprayed some penetrate on the stud shielding the surrounding areas from over spray.
3.
Hammered it out with a 2 pound hammer. A dead blow hammer may have worked well, but I didn't have one. I placed a piece of 2x4 against the end of the axle to guide the hammer to the stud (not pictured, I only have 2 hands!).

Here's a picture of the old and new stud.

4.
Turned the axle until the hole was lined up with an area where the breaks had enough room to slide the stud in from the back.

5.
Put on several washers and an open end lug nut. I used the flat side against the washers. Tightened to specified torque. As it tightened it drew the stud into the axle flange.
I then removed the nut and washers. Measured the length of the stud against the others. It was the same length.

7.
Put drum and wheel back on. Took vehicle off jack stands. Unchalked front wheels. I used anti-seize on the lug nuts and tightened 20% less than specified torque.
Fin!